Abstract
So much use is being made of number lines these days that it may not occur to elementary teachers to represent numbers in other ways. There are, in fact, many ways to picture whole numbers geometrically as arrays of squares or triangles or other shapes. Often, important insights into, for example, oddness and evenness can be gained by such representations. The following account of a sixth-grade class discussion of fractions shows how a “number pencil” can be constructed to represent all the positive rational numbers, and, by a similar method, also the negative rationals. An extension of this could even be made to obtain a number pencil picturing certain irrational numbers.
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